Discrete direct and adjoint sensitivity analysis for arbitrary Mach number flows

Parallel discrete direct and adjoint sensitivity analysis capabilities are developed for arbitrary Mach flows on mixed-element unstructured grids. The discrete direct and adjoint methods need a consistent and complete linearization of the flow-solver to obtain accurate derivatives. The discontinuous nature of the commonly used unstructured flux-limiters, like Barth–Jespersen and Venkatakrishnan, make them unsuitable for sensitivity analysis. A modification is proposed to make these limiters piecewise continuous and numerically differentiable, without compromising the monotonicity conditions. An improved version of Symmetric Gauss–Seidel that significantly reduces the computational cost is implemented. A distributed-memory message passing model is employed for the parallelization of sensitivity analysis solver. These algorithms are implemented within a three-dimensional unstructured grid framework and results are presented for inviscid, laminar and turbulent fl